Monthly Archives: May 2017

The first challenge that popped into my mind when asking myself this question was that many activities that can come from STEM challenges need access to a variety of resources (i.e. technology!). That being said, many resources can come from such things like recycled materials, but when particular items need to be bought, it is not necessarily in the classroom or school budget and generally comes out of the teacher’s pocket. Bybee (2013) discusses how not having access to technology is one of the main issues when trying to incorporate STEM into the classroom. Beyond having access to technology, there are many other conceptual challenges with regards to STEM that have more to do with the students than the resources available.

In the video A Private Universe we were asked to witness numerous conceptual challenges. The video explores a local high school to see if the students have correct assumptions with regards to various scientific topics. Heather, a Grade 9 student, from a local high school was chosen by her teacher as someone who would most likely have a good answer for any scientific question asked. What the teacher did not realize was that Heather had virtually no knowledge with regards to science and more specifically the phases of the moon. Heather sat through a secondary lesson on the phases of the moon and was then re-interviewed 2 weeks later. However, as her private theories were still very much evident, Heather did not accept the correct information on the phases of the moon.

This made me reflect of the importance of diagnostic assessments. Teachers need to be aware of what their students know with regards to starting a new topic/discussion. Without understanding where a student is at, how can one program effectively and make sure that all the students are on the right track with their understanding?

Tabula Rasa, a blank slate, is certainly not the case with students, especially students in high school. Catherine Fosnot (2013) describes education and constructivism by saying that “too often teaching strategies and procedures seem to spring from the naïve assumption that what we ourselves perceive and infer from our perceptions is there, ready-made, for the student to pick up, if only they had the will to do so” (p15). Heather came to the class with pre-existing notions that were not addressed at the very beginning of the lesson or unit and as such, she is holding onto her private theories tightly. In the Confrey (1990) article, he mentions a quote by Osborne and Wittrock (1983) that states, “children develop ideas about the world, develop meanings for words used in science [mathematics and programming], and develop strategies to obtain explanations for how and why things behave as they do” (p. 4). Heather developed pre-existing ideas about the phases of the moon and has believed that for so many years that it is now difficult, half way through the unit, to switch her thinking.

References

Bybee, R.W. (2013). A Case for STEM Education: Challenges and Opportunities. United States of America: National Science Teachers Association.

Confrey, J. (1990). A review of the research on student conceptions in mathematics, science, and programming. Review of research in education, 16, 3-56. http://ezproxy.library.ubc.ca/login?url=http://www.jstor.org/stable/1167350

Fosnot, Catherine. Constructivism: Theory, perspectives, and practice. Teachers College Press, 2013 or 2005 version. Chapter 1: Introduction: Aspects of constructivism by Ernst von Glasersfeld or Chapter 2: Constructivism: A Psychological theory of learning or Cobb, Paul. “Where is the mind? Constructivist and sociocultural perspectives on mathematical development.” Educational researcher 23, no. 7 (1994): 13-20. Available in the course readings library.

Schneps, Matthew. (1989). A Private Universe: Misconceptions That Block Learning. Retrieved from: http://learner.org/vod/vod_window.html?pid=9

Once I got over the hair and trying to identify the decade in which the video was shot, I was pretty captivated by the developmental path of Heather’s concept of an orbit.

Because of the montage style of filming, it is quickly apparent that Heather comes to the class with preconceived, informal notions about the movement of planets.  Having taught astronomy, I can attest to there being a ton of information, much of it highly graphical and spread over thousands of years of history and many cultures.  In this case,  she has superimposed orbital motion with formal learning about the analemma—the relative position of the Sun at noon every day over the course of a year.

I was further struck by the importance of clear graphical representation as illustrated by the “perspective view” of a circular orbit appearing to be an ellipse.  At the time of this writing, a Google image search for “orbital motion” delivered this gem:

Hosted proudly on PowerSchool Learning the curriculum clearly shows the Earth in a highly (incorrect) eccentric orbit.  For extra irony, there is a link to a PhET animation, arguably the most reliable and accurate simulation space for physics on the web today.

In my exploration of the readings around conceptual challenges I find the “formal versus informal knowledge gap” the most compelling.  If formal describes the white-washed, devoid of context topics like “block on an incline” from a standard introduction to physics, then informal is all of the real sensory concepts and language that people develop to explain what they experience in “real life”.  Why can’t we spend more time meeting the kids where they are and give them more time to explore?  Learn about things that are directly relevant to the structures that they live within?  Watching Heather come to an astronomy class and “book learn” about things she cannot touch or clearly observe directly to me is just another example in a career litany of curriculum that is divorced from practical application for the sake of, say, academic purity, or following an “accretion of knowledge” paradigm that is demonstrably not very effective for many learners.

British Columbia is going through an interesting change in curriculum that offers an opportunity to address this formal/informal gap.  In broad strokes, the focus has changed from curriculum heavy with “things to be taught” to a reduced list of core competencies and the chances to explore concepts in a way that is deeper and more personally relevant.  Although the details and execution are in early days, I believe this is the best chance we’ve had to move the focus of school from teacher-centred to valuing student-centred study.  It is my hope that allowing for differentiated instruction and more time to learn, students will have a chance to reduce the formal/informal gap.

Confrey, J. (1990).  A Review of the Research on Student Conceptions in Mathematics, Science, and Programming.  Review of Research in Education, Vol. 16 pp. 3-56.

Technology with its wide adoption and ease of use brings with it great opportunity but also presents a challenge to educators.  Our ability to share ideas to a large audience is easier than ever and thus we find ourselves with the challenge of filtering false ideas from our students.  Further, students arrive in our classrooms with their own experiences and misconceptions of ideas we are attempting to build on, challenging the educator to cover course content yet also ensure students are developing deep, meaningful learning.

Fosnot (2013) describes behaviorism and maturationism as two theories of learning that educators use to either help students understand concepts or determine when it may be appropriate for them to cover that material.  Behaviorism, specifically reinforcement and practice, is a pedagogical approach many math teachers, including myself have used to develop student understanding of specific ideas.  The problem arises if these methods of teaching are used to help students memorize procedures without any attempt to ask the question why?.  The third theory, Constructivism, addressed this problem directly.  It is a widely studied theory that states students construct their deep knowledge on a particular topic through experience and reflection.  Further, the new knowledge is built on top of previous knowledge again demonstrating the importance of educators addressing student misconceptions early.

In our course video, we learned that regardless of their science education, twenty one of twenty three Harvard graduates had misconceptions about the phases of the moon and why we have seasons on earth.  The video went on to focus on a grade 9 student, Heather, why had some interesting ideas on the same question.  We saw that Heather had much of the terminology correct but didn’t fully understand what the terms meant (indirect and direct sunlight for instance).  After classroom instruction on the topic, Heather was able to reverse some of her misconceptions but even after direct, one on one instruction, Heather was not willing to let go of some ideas she had formed.  

We, as educators, have great resources at our disposal to help students develop deep understanding of our course content and curricular competencies.  We have lesson videos such as Khan Academy and free graphing tools such as Desmos.com to allow students to manipulate equations and see the impact these manipulations have graphically.  Accurate simulations are available for almost every subject area (I teach business education and there are a wealth of simulations available to educators) and are generally free to use.  Ellis et. al. (2011) studied students experiences using technology in the science, math and history classes and found that students engaged highly (for different reasons depending on the subject) with the content.  One of the findings was that students appreciated the wider range of answers they could find on the internet and thus potentially increasing the chances of developing a deeper understanding.

References

Constructivism: A Psychological theory of learning or Cobb, Paul. “Where is the mind? Constructivist and sociocultural perspectives on mathematical development.” Educational researcher 23, no. 7 (1994): 13-20. Available in the course readings library

Ellis, R., Goodyear, P., Bliuc, A., & Ellis, M. (2011). High school students’ experiences of learning through research on the Internet. Journal Of Computer Assisted Learning, 27(6), 503-515. doi:10.1111/j.1365-2729.2011.00412.x

Fosnot, C. T. (2013). Constructivism: Theory, perspectives, and practice. Teachers College Press.

Watching the video provided this week and seeing some of the common misconceptions that even the most educated students have about the solar system reminded me of a recent misconception that was shared among my grade 8 students about the concept of repeated multiplication.  In the video, Heather’s misconceptions of the videos stem from misinterpretations of common illustrations used in textbooks, and a misconstrued view of the solar system and its planetary bodies. I find my own student’s misunderstanding to have similar causes.

The problem that my students struggled with this year had to do with an application of exponents, specifically with the number of bacteria in a population after it has undergone a period of exponential growth. The problem I pose to students is as follows:

“In the beginning of an experiment, there is 50 bacteria cells. The bacteria population grows when each bacteria splits in half. How many bacteria would there be after 4 divisions?”

A common solution given by my students is as follows: “50 * 50 * 50 * 50 = 6250000, so there are 62500000 bacteria after 4 divisions”

This calculation is incorrect because the concept of splitting in half cannot be captured directly by multiplying the initial population repeatedly. The correct solution would be that “50 * 2 * 2 * 2 * 2 = 800 bacteria”

One may classify this type of error as an error due to “rigidity of thinking leading to inadequate flexibility in decoding and encoding new information” (Comfrey, 1990) When students are first introduced to exponents, they are usually taught the “fact” that for a given number n, n^m = n * n * n * n m times, usually without any accompanying illustrations or physical models, thus it could become very difficult to come up with different ways of using that rule. As constructivists would have it, the individual mental construction of the concept is largely incomplete. (Cobb, 2004)

In order to better integrate this knowledge and apply it to bacteria growth, students need time to reflect on their solution in different ways (Davis, 2000). The students should be encouraged to ask themselves, “Is it plausible for 50 bacteria to turn into 62500000 bacteria just after 4 divisions?”, “If the same pattern was consistent, would 3125000000 bacteria after 5 divisions make sense?” Students should be asked not only to reflect on this through thinking, but also through illustration. How would one draw a bacteria population of 62500000? How does this drawing compare to that of 50 bacteria?

In order to solve the given problem, different strategies should be taught in addition to the rule. Some of which include drawing pictures depicting the number of bacteria after each split, or constructing a table to record the number of bacteria after each split. Other strategies involving digital technology would be showing videos or animations of bacteria growth in order to further help students in developing their understanding of exponential growth. I believe these are all strategies that will assist in helping students develop a more accurate model of knowledge.

Cobb, P. (1994). Where is the mind? Constructivist and sociocultural perspectives on mathematical development. Educational researcher, 23(7), 13-20.

Confrey, J. (1990). A review of the research on student conceptions in mathematics, science, and programming. Review of research in education, 16, 3-56.

Davis, E. A. (2000). Scaffolding students’ knowledge integration: Prompts for reflection in KIE. International Journal of Science Education, 22(8), 819-837.

In A Private Universe, students and faculty are asked to explain their reasoning for various scientific concepts. Heather is identified by her science teacher as being the student who she would expect to “give a better explanation than the other kids could.” Despite the assumption that Heather has all the correct answers, when prompted, Heather’s prior knowledge and exposure to the scientific concepts from external sources creates for her several misconceptions about the rotations of the Earth, the phases of the moon and the properties of light in space. With further provocation and physical tools, Heather is able to readjust her hidden misunderstandings to match the scientific concepts more accurately. Her confrontation of her misconceptions prompt her to find new, true meanings within the concepts.

Further on, however, Heather is still unable to let go of her private theories regarding light, despite a one-on-one lesson. Rosalind Driver (1985) address this refusal of change as part of the private theories being stable. While students may learn new concepts, they are not a blank slate. They may, therefore, ignore counter-evidence towards their perceived theory or alter their theory to fit the new information, rather than refute a construct they have built up in their minds previously (Driver, 1985).

This is something I have witnessed within the classroom as an educator. Students have been introduced to the word “hacking” and many of them have had different experiences related to this. While attempting to teach a lesson on coding, as a way of giving instructions to produce a result, a student raised his hand and asked if coding was like hacking? This drove us to have a meaningful conversation around internet safety, however, by the end of the lesson I could tell that there were still a few confused faces when being confronted with the word “hacking”.  It wasn’t until the students engaged in meaningful activities around coding that they were able to correct their misunderstandings about coding and hacking being similar (Shapiro, 1988). Through a study conducted on university students, active learning was found to be the most effective in solidifying conceptual understandings in STEM related fields, regardless of class size or the particular STEM discipline (Freeman et al., 2014). Therefore, meaningful engagement and active learning with the concepts being studied may be the best way to help students overcome misconceptions and challenge their private theories.

When it comes to technology, having students engage with the material themselves may create a more solid understanding than a PowerPoint or video. Students can be challenged to prove their private theories by creating tutorial videos or explanatory animations where they need to interact with both the concepts and the technology to make a concept “make-sense” for someone other than themselves. Not only will this aid in further instruction by knowing where they might be coming from with their prior knowledge, but it will also clarify for themselves areas that lack a complete understanding.

Driver, R. Guesne, E. & Tiberghien, A. (1985). Children’s ideas and the learning of science. Children’s ideas in science, 1-9.

Freeman, S., Eddy, S. L., McDonough, M., Smith, M. K., Okoroafor, N., Jordt, H., & Wenderoth, M. P. (2014). Active learning increases student performance in science, engineering, and mathematics. Proceedings of the National Academy of Sciences, 111(23), 8410-8415.

Shapiro, B. L. (1988). What children bring to light: Towards understanding what the primary school science learner is trying to do. Developments and dilemmas in science education, 96-120.

Schneps, Matthew. (1989). A Private Universe: Misconceptions That Block Learning. Retrieved from: http://learner.org/vod/vod_window.html?pid=9

In the video A Private Universe, Heather articulates personal theories regarding several natural phenomena. Heather has developed many misconceptions that she uses to explain the world around her. Her teacher is surprised when she expresses detailed an understanding not connected with content and explanations introduced in class.  Osborne and Wittrock (1983) write that “children develop ideas about their world, develop meanings for words used in science [mathematics and programming], and develop strategies to obtain explanations for how and why things behave as they do” (p. 491). Heather has many private theories and through verbal explanation and drawing, Heather becomes aware of her prior knowledge. She did seem somewhat unsure and dissatisfied with her explanations. Heather was able to reverse her misconceptions through new experiences in the classroom.  Posner writes that “a new conception is unlikely to displace on old one, unless the old one encounters difficulties, and a new intelligible and initially plausible conception is available that resolves these difficulties.” (p. 219). She confronts her private theory and is able to accommodate a new understanding. In A Review of the Research on Student Conceptions in Mathematics, Science, and Programming (1990) Confrey writes “teachers are often, and understandably, impatient for their students to develop clear and adequate ideas. But putting ideas in relation to each other is not a simple job. It is confusing; and that confusion does take time. All of us need time for our confusion if we are to build the breadth and depth that give significance to our knowledge” (p.  9). This demonstrates the importance of activating prior knowledge and engaging in activities that might cause conflict within the learner.

During the video and the articles, I was connecting to the program First Steps in Math which has helped me identify many mathematical misconceptions students hold. It is all about identifying student’s misconceptions about math and having them explain and confront their thinking. When I took the PD several years ago they highlighted examples of several children using personal theories to solve math problems. Most of the teachers at the PD initially assumed the students were randomly attempting solutions. However, through the case studies, it was demonstrated that the kids had developed, although very misguided, ideas and procedures they were applying very purposefully. In one place value assessment from the program, kids have to identify the number of dinosaurs in the picture below. When they determine that there are 35 dinosaurs, they are asked to underline the 35 (without the teacher identifying the number). They are then asked to circle that many dinosaurs. The majority of the teachers said most of their kids circled 3 instead of 30 dinosaurs. It then recommends a series of activities that help address student’s misconceptions about the number system.

I think technology can be very useful to help kids address conceptions. I now usually start new math and science concepts with a chance for students to explain and demonstrate their prior knowledge and personal theories on the subject. When studying the human body my students used Explain Everything to collaboratively create videos about what they thought happened to food after they ate it. It is very interesting to hear their ideas and attempts to explain their thinking. Many came out of the project with a pretty accurate understanding before we even “started”, just through collaboration with knowledgeable students.  Technology can also allow students to manipulate visualizations or participate in online environments that provide immediate feedback, allowing them to continually test their thinking.

Confrey, J. (1990). A review of the research on student conceptions in mathematics, science, and programming. Review of research in education, 16, 3-56. http://ezproxy.library.ubc.ca/login?url=http://www.jstor.org/stable/1167350

Posner, G.J., Strike, K.A., Hewson, P.W., and Gertzog, W.A. (1982). Accommodation of a scientific conception: Toward a theory of conceptual change. Science Education, 66, 211-227.